Matrices

Front

What are matrices?

Back

Matrices are rectangular arrays of numbers, symbols, or expressions, arranged in rows and columns.

Front

What is the dimension of a matrix?

Back

The dimension of a matrix is defined by the number of rows and columns it contains, expressed as 'rows x columns'.

Front

Can you multiply a 2x3 matrix by a 3x2 matrix?

Back

Yes, you can multiply a 2x3 matrix by a 3x2 matrix, resulting in a 2x2 matrix.

Front

What is the result of multiplying a 2x3 matrix by a 3x12 matrix?

Back

The result will be a 2x12 matrix.

Front

What is the product of the following matrices: [[1, 2, 3], [4, 5, 6]] and [[7], [8], [9]]?

Back

The product is [[50], [122]].

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all the elements are zero.

Front

How do you find the transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows with its columns.

Front

What is the determinant of a 2x2 matrix [[a, b], [c, d]]?

Back

The determinant is calculated as ad - bc.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that AA^-1 = I, where I is the identity matrix.